Sorry to kill your joy, but yeah, Shiny WISHMKR Jirachi, even legitimate ones, won't go through Pokebank/Transporter. I should know, as I have one.
Normal WISHMKR Jirachi will go through, shiny ones however, will not.
A shiny one is never considered as legitimate by Game Freak, it can't even be uploaded into 5th Gen GTS, in the same way you cannot trade away a Level 9 or under Resh/Zek.
From what I've heard, the reason why it is not considered as legitimate, is because it was never meant to be able to shine. Apparently, while all the other Pokemon has 1 shiny check (that is a check that determines whether a Pokemon is shiny or not), this Jirachi has 2. It is possible that the 2 shiny check is meant to make it way harder to get a shiny one, as you're dealing with 1/8192 being rolled twice. If the first check produces a shiny, the second check will roll, and will most likely change the result of the first check. Therefore, while it is still possible to obtain a shiny (on the second check), the chance of it happening is so slim you might as well consider it not possible - you basically have to encounter two shinies in a row with the standard 1/8192 chance.
However, people eventually found a way to bypass the double shiny check, iirc it was through some kind of RNG abuse.
I think that's what makes GF create and implement shiny lock, which instead of making it harder to get a shiny, it completely lock the shiny form out by having 1 check that always roll again if it produces a shiny - basically, an infinite shiny check.
Another theory I've also heard is that the Jirachi already has a shiny lock on it - it's just not activated for whatever reason, probably the programmer forgot to activate it.
That would also explain why GF refuse to admit Shiny Jirachi is possible - because it was supposed to be not possible to shine.
In addition to that, there are only 9 possible Natures for a Shiny Jirachi due to how the system works back then, which somewhat makes it even harder to get a shiny one.
